Problem: Simplify the following expression: $t = \dfrac{3q^2 - 18q + 24}{q - 2} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ t =\dfrac{3(q^2 - 6q + 8)}{q - 2} $ Then we factor the remaining polynomial: $q^2 {-6}q + {8} $ ${-2} {-4} = {-6}$ ${-2} \times {-4} = {8}$ $ (q {-2}) (q {-4}) $ This gives us a factored expression: $\dfrac{3(q {-2}) (q {-4})}{q - 2}$ We can divide the numerator and denominator by $(q + 2)$ on condition that $q \neq 2$ Therefore $t = 3(q - 4); q \neq 2$